I'd like to migrate my photo library out of Aperture, but still use it to edit photos (maybe). I'd like to export the masters and the modified versions of all my photos into standard Finder folders in the format YYYY/MM/DD. I can't seem to find any advice on how to do that.

If no plugin is found that does what you want, you could also try to write up an Automator workflow. Here's an example workflow. It does not do exactly what you want, but it contains information regarding the Automator and Aperture pairing.
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Bart ArondsonApr 1 '12 at 9:16

AmoK Exif Sorter cannot only rename pictures. The software can also
move or copy them to arbitrary folders. These folders again, can be
named according to the exif data. For instance, all pictures taken in
February 2007 could be moved to c:fotos2007February and the pictures
named according to the template "year-month-day_time_some-text" which
would result in a file name such as 2007-02-27_18:34_New_York.jpg.

I agree with Rob that a two-pronged approach might be easiest. He suggests specific software, but it an actually be generalized:

Export from Aperture into whatever format it wants (ideally making sure to have no duplicate base names, regardless of folder structure).

Use any bulk photo rename program to rearrange into the folder structure.

For example, you can use the free, cross-platform command-line tool jhead to do step 2. For step 1, export all of the photos to one huge folder. Then, get jhead, open a terminal window, cd to the directory containing all of your jpegs, and run:

head -nf'%Y/%m/%d/%f *.jpg

This will take all of the .jpg files in that directory and move them into a nested folder structure as you describe, followed by the original filename (that's the %f). Jhead will create the folders as needed.

Pretty much any bulk rename tool will work — if you're comfortable with the command line, jhead is an easy free choice. If you're looking for a GUI option... take your pick.